Question

A large flexible protein can take on 10^25 conformations of the same energy. A) Determine the entropy of the protein. B.If this protein interacts with a substrate, it is now only able to adopt 10^10 conformations of the same energy. Calculate the change in molar entropy of this transition.

Answer 1

Answer :

(A) : according to statistical thermodynamics , entropy is given as

S = k * ln w

w = no. of conformation = 10²⁵

k = Boltzmann constant = 1.38 * 10^-23 J/K-mol

S = k * 2.303 * log (w) = 1.38 * 10^-23 * 2.303 * log ( 10²⁵) = 79.45 * 10^-23 J /K-mol

(B) : now ,

w = 10¹⁰

So, entropy (S) = k * 2.303 * log (w) = 1.38 * 10^-23 * 2.303 * log(10¹⁰) = 1.38 * 10^-23 * 2.303 * 10 = 31.78 * 10^-23 J/K-mol

Change in entropy = 79.45 * 10^-23 - 31.78 * 10^-23 = 47.67 * 10^-23 J/K-mol